Title	Colorful Helly-type Theorems for Ellipsoids
Creator	Naszodi, Marton
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-10-08T09:47
Description	We prove the following Helly-type result. Let $\mathcal{C}_1,\ldots,\mathcal{C}_{3d}$ be finite families of convex bodies in $\mathbb{R}^d$. Assume that for any colorful choice of $2d$ sets, $C_{i_k}\in \mathcal{C}_{i_k}$ for each $1\leq k\leq 2d$ with $1\leq i_1< \ldots < i_{2d}\leq 3d$, the intersection $\bigcap\limits_{k=1}^{2d} C_{i_k}$ contains an ellipsoid of volume at least 1. Then there is a color class $1\leq i \leq 3d$ such that $\bigcap\limits_{C\in \mathcal{C}_i} C$ contains an ellipsoid of volume at least $d^{-O(d^2)}$. Joint work with GÃ¡bor DamÃ¡sdi and ViktÃ³ria FÃ¶ldvÃ¡ri.
Extent	34.0 minutes
Subject	Mathematics; Geometry; Convex and discrete geometry; Discrete mathematics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Eötvös University
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2020-04-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0389741
URI	http://hdl.handle.net/2429/73912
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos